Sears department is seen in Hackensack, N.J. Eddie Lampert and his ESL Holdings hedge fund are offering to buy the rest of Sears for up to $4.6 billion in cash and stock.

Eddie Lampert and his ESL Holdings hedge fund are offering to buy the rest of Sears for up to $4.6 billion in cash and stock.

The Sears chairman and ESL own just under half of the Hoffman Estates, Illinois, company, according to FactSet. Sears filed for Chapter 11 bankruptcy protection in October, weighed down by years of declining sales and massive debt.

ESL Holdings said in a regulatory filing Thursday that its nonbinding offer for roughly 500 remaining Sears stores will keep about 50,000 employees working. The offer is subject to due diligence and ESL's ability to get financing, among other things.